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Download Differential geometry, Valencia 2001 : proceedings of the by O Gil-Medrano; Vicente Miquel; A M Naveira (eds.) PDF

By O Gil-Medrano; Vicente Miquel; A M Naveira (eds.)

This publication provides a concise yet systematic account of the formation of spatial movement buildings in a horizontal fluid layer heated from less than. Flows of this kind, often called Rayleigh-Benard convection, express vital gains of behaviour inherent not just in quite a few hydrodynamic-instability phenomena but additionally in nonlinear pattern-forming strategies in different contexts. The e-book describes the fundamental tools of investigating convection styles and the kinds of 2- and 3-dimensional flows, trend defects, and sequences of convection-regime adjustments. the writer will pay unique realization to the query of the way different factors (mainly reducible to preliminary and boundary stipulations) make sure the sizes and shapes of the constructions which enhance. during this means, the position of order and illness in circulation styles, as an element strongly affecting the nature of the evolution of buildings, is printed. The presentation emphasizes the actual photograph of those phenomena, with no over the top mathematical element

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Read or Download Differential geometry, Valencia 2001 : proceedings of the international conference held to honour the 60th birthday of A.M. Naveira, Valencia, July 8-14, 2001 PDF

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Additional resources for Differential geometry, Valencia 2001 : proceedings of the international conference held to honour the 60th birthday of A.M. Naveira, Valencia, July 8-14, 2001

Example text

It then follows that A / = Az - nHu + V 2 / ( N , N), and V 2 / ( W , N) = (Vu, Vz) + (A(Vz), Vz) + u V 2 / ( N , N) = div(uVz) - uAz + (A{Wz), Vz) + u V 2 / ( N , N ) , where div stands for the divergence operator on M. Finally, this allows us to rewrite formula (5) as (4). What is really ingenious in Reilly's argument is the way to use (4) in order to study the geometry of the boundary. To see it, let us consider / € C°°(f2) the solution of the following Dirichlet problem A / = 1 in fl and / = 0 on M = 89..

If x denotes the position vector in K n + 1 , then A(x, x) = 2(n + 1), where A denotes the Euclidean Laplacian on R n + 1 . N)dM = 0, (3) JM where V(Cl) is the (n + l)-dimensional volume of Q,. The integral formulae (2) and (3) are one of the essential ingredients in Reilly's proof. The other one is a new integral formula established by Reilly in [40], which for the case of Euclidean hypersurfaces states as follows. Theorem 4 (Reilly's formula) Let M a compact hypersurface embedded in R™+1, bounding a compact domain ft, dil = M.

G A L V E Z Departamento de Geometria y Topologia, Universidad 18071 Granada, Spain E-mail: jagalvez@ugr. es de Granada, In this work we prove t h a t the only compact spacelike surfaces in the 3-dimensional de Sitter space with a constant principal curvature are the totally umbilical round spheres. We also characterize the totally umbilical round spheres of the 3-dimensional de Sitter space as the only compact linear Weingarten spacelike surfaces. As a consequence, we show that the only compact linear Weingarten surfaces in the 3-dimensional hyperbolic space with non-degenerate second fundamental form are the totally umbilical round spheres.

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